Question

Suppose today two-year US treasury bill is 2.15% and the two-year UK treasury bill is 1.0%. Further suppose today spot exchange rate is USD 1.25 per Euro and you know you will receive one million euro exactly two years from now and you will have to exchange those Euros in USD at that time. Can you engineer a guaranteed exchange rate at which you will be able to exchange the Euros for USD two years from now? Explain the arrangements.

Answer 1

In order to guarantee an exchange rate after two years, one needs to implement a money-market hedge which can be executed as described below:

- EUR Receivable = 1000000 EUR, EUR Interest Rate = 1% and Tenure = 2 years.

- Present Value (PV) of EUR Receivable = 1000000 / (1.01)^(2) = 980296.0494. Borrow an EUR amount equal to this PV of EUR receivables (i.e borrow 908296.0494 EUR)

- Convert this EUR borrowing into USD at the current exchange rate of 1.25 USD/EUR to yield = (980296.0494) x 1.25 = $ 1225370.062

- Invest the converted $ worth $ 1225370.062 for two years at the US interest rate of 2.15 % to yield = (1225370.062 x 1.0215 x 1.0215) = $ 1278627.402

- The investor's original EUR borrowing creates a payment liability worth EUR 1000000 after 2 years which can be paid off using the fixed EUR receivable, while the investor can keep the $ investment.

- This arrangement creates a situation wherein the investor retains $ 1278627.402 while paying EUR 1000000, thereby guaranteeing an exchange rate of (1278627.402/1000000) = $ 1.278627402/ EUR